The Held—Karp algorithm and degree-constrained minimum 1-trees Authors Short Communication

Received: 01 August 1977 Revised: 08 May 1978 DOI :
10.1007/BF01609023

Cite this article as: Yamamoto, Y. Mathematical Programming (1978) 15: 228. doi:10.1007/BF01609023
Abstract In this note we propose to find a degree-constrained minimum 1-tree in the Held—Karp algorithm [5, 6] for the symmetric traveling-salesman problem, and show that it is reduced to finding a minimum common basis of two matroids.

Key words Traveling-Salesman Problem 1-tree Matroid

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M. Held and R.M. Karp, “The traveling-salesman problem and minimum spanning trees: part II”,Mathematical Programming 1 (1971) 6–25.

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M. Iri and N. Tomizawa, “An algorithm for finding an optimal ‘independent’ assignment”,Journal of the Operations Research Society of Japan 19 (1976) 32–57.

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© The Mathematical Programming Society 1978